is false if $E=\ell^{1}\left(\Gamma\right)$,
and $F=c_{0}\left(\mathbb{N},H\right)$, where $H$ is a Hilbert space,
and both $\mid\Gamma\mid$and $dens$ $H$ are big enough. My [maybe
rather vague] question would be: are there some known (and non-trivial)
sufficient conditions on the pair $\left(E,F\right)$ s.t. $\mathcal{P}_{E,F}$ is
true ? Thx in advance.

I suppose the reason I cannot see that question 23221 has the consequences you state is that I am about ready to fall asleep, so I won't ask about that. Instead, I'll ask this: What is this thing you call $dens$ $H$?
–
Harald Hanche-OlsenMay 3 '10 at 2:13